ENVIRONMENTAL MANAGEMENT POLICY UNDER INTERNATIONAL CARBON LEAKAGE

INTERNATIONAL ECONOMIC REVIEWVol. 54, No. 3, August 2013

ENVIRONMENTAL MANAGEMENT POLICY UNDER INTERNATIONALCARBON LEAKAGE∗

BY KAZUHARU KIYONO AND JOTA ISHIKAWA1

Waseda University, Japan; Hitotsubashi University, Japan

This article studies environmental management policy when two fossil-fuel-consuming countries noncooperativelyregulate greenhouse-gas emissions through emission taxes or quotas. The presence of carbon leakage caused by fuel-price changes affects the tax-quota equivalence. We explore each country’s incentive to choose a policy instrument in atwo-stage policy choice game and find subgame-perfect Nash equilibria. This sheds new light on the questions of whichpolicy instrument is more stringent and of why adopted instruments could be different among countries. In particular,our result suggests a reason why developing countries tend to employ emission taxes whereas developed countries tendto adopt quotas.

1. INTRODUCTION

To tackle the issue of global warming, the Conference of the Parties (COP) to the UnitedNations Framework Convention on Climate Change has been meeting annually since 1995.In 1997, the third meeting, the COP 3, adopted the Kyoto Protocol, in which the developedcountries, called Annex I Parties to the Convention, made a commitment to decrease theirgreenhouse gas (GHG) emissions to 5.2% below their 1990 baseline levels over the 2008–2012period. However, Non-Annex I Parties have no obligation to the reductions. Governments ofAnnex I Parties have gradually adopted measures to reduce GHG emissions. For example,emissions trading has been implemented by the EU and New Zealand. Emission taxes havebeen introduced in Australia.2

Since the Kyoto Protocol expires at the end of 2012, the post-Kyoto Protocol deals havebeen negotiated. The COP 17, held in Durban, South Africa, in 2011, agreed to the DurbanPlatform that a legally binding deal comprising all countries be prepared by 2015 to put it intoeffect in 2020. Therefore, not only developed countries but also developing countries have toadopt some measures to control GHG emissions. In fact, India and South Africa have alreadyintroduced an emission tax. China has also announced that it will implement an emission tax by2015.

A major element of measures to control GHG emissions adopted by many countries isthe introduction of emission taxes and quotas (including the creation of markets to tradeemission permits). Previous studies on environmental regulation suggest that, within a closedeconomy, emission taxes and quotas are essentially equivalent instruments. In an open-economy

∗Manuscript received November 2011; revised July 2012.1 We wish to thank three anonymous referees, Shunsuke Managi, Shiro Takeda, and participants of APTS and

Australasian Trade Workshop and of seminars at Keio University, Kobe University, the Norwegian School of Economicsand Business Administration, Stockholm University, and Tohoku University for their helpful comments on earlierversions of this article. The usual disclaimer applies. We are grateful to Ralph Paprzycki for editing this paper. Ishikawaacknowledges financial support from the Ministry of Education, Culture, Sports, Science and Technology of Japan(MEXT) through a Global Center of Excellence Project and a Grant-in-Aid for Scientific Research (A). Ishikawadedicates this article to the late Professor Kazuharu Kiyono, who passed away before this article was completed. Pleaseaddress correspondence to: Jota Ishikawa, Faculty of Economics, Hitotsubashi University, Kunitachi, Tokyo 186-8601,Japan. Fax: +81-42-580-8882. E-mail: [email protected].

2 In Australia, emission taxes will be replaced by emissions trading in 2015. The United States, which is a signatoryto the protocol, has not ratified the protocol.

1057C© (2013) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Socialand Economic Research Association

1058 KIYONO AND ISHIKAWA

framework, however, this is usually not the case. In particular, carbon leakage across countriescould arise and affect the equivalence.

An important point in an open-economy framework is that the toughness of each country’santi-global-warming policies is affected by the policy choices of other countries, in turn affectingglobal environmental quality. For example, the emission regulations adopted by one countrydo not affect GHG emissions of other countries if these countries employ emission quotasthat are binding. That is, international carbon leakage does not occur once other countriesdirectly control their GHG emissions. As Kiyono and Ishikawa (2003) pointed out, emissiontaxes and quotas are unilaterally equivalent for each country given the policy decisions of othercountries (unilateral equivalence). However, they are not unilaterally equivalent once eachcountry understands that the policy instrument choices of other countries may be affected byits own choice under strategic interdependence among countries subject to the carbon-leakageeffect (strategic nonequivalence).3

In this article, we first demonstrate unilateral equivalence and strategic nonequivalence morerigorously in the presence of international carbon leakage.4 We should mention that in ourstudy, the term “tax-quota equivalence” is understood to mean that subject to the objectiveof national welfare maximization, the government can achieve the same resource allocationthrough either an emission tax or an emission quota. However, the term has several differentmeanings in the previous literature, in particular, when the replacement of an emission taxwith a quota that is set to equal emission levels under the tax-ridden equilibrium gives rise tothe same resource allocation across the economy. Within a partial equilibrium framework inthe absence of uncertainty and incomplete information, such equivalence holds in a perfectlycompetitive market (see Xepapadeas, 1997) as well as in an imperfectly competitive marketwithout strategic abatement investment by firms before the government policy decision (seeUlph, 1996). However, the equivalence breaks down in a general equilibrium model, as shownin Ishikawa and Kiyono (2000, 2006) and Ishikawa and Okubo (2008).5 This is mainly becausean emission quota puts a cap on a country’s total GHG emissions whereas the emissions areendogenously determined under emission tax policy.

When the equivalence does not hold, interesting research questions are (i) which policyinstrument is more stringent and (ii) why some countries adopt emission taxes whereas othersadopt emission quotas. We then address these questions. We explore each country’s incentive tochoose an environment regulation instrument within a framework of a two-stage policy choicegame and find subgame-perfect Nash equilibria.

Carbon leakage across countries plays a crucial role in our analysis. There are three mainchannels through which international carbon leakage can arise. The first channel is changes ina country’s industrial structure, as discussed in Copeland and Taylor (2005) and Ishikawa et al.(2012). When a country adopts emission regulations, the comparative advantage of the emission-intensive industry could shift abroad. The second channel is the relocation of plants in responseto emission regulations, particularly in emission-intensive industries (see Markusen et al., 1993;Markusen et al., 1995; Ulph and Valentini, 2001; Ishikawa and Okubo, 2008, for example). Thethird channel is, finally, the changes in the price of fossil fuels (see, e.g., Bohm, 1993; Felderand Rutherford, 1993; Burniaux and Martins, 2000; Kiyono and Ishikawa, 2003; Hoel, 2005;Boringer et al., 2010). A decrease in fossil fuel demand caused by emission regulations in onecountry lowers the global price of fossil fuels, boosting fossil fuel demand and, hence, GHGemissions in other countries.

3 The issue of unilateral equivalence and strategic nonequivalence between tariffs and quotas was discussed in Kiyono(1985).

4 In Kiyono and Ishikawa (2003), we discussed the issue of unilateral equivalence and strategic nonequivalence.However, the analysis there was conducted in a much simpler framework using partial equilibrium analysis. In additionto providing a general equilibrium analysis, this study analyzes the game of policy instrument choices.

5 Even in the absence of carbon leakage, the tax–quota equivalence may break down. Whereas a difference inpollution intensities across industries plays a crucial role in Ishikawa and Kiyono (2000, 2006), firm relocation (i.e.,foreign direct investment) is crucial in Ishikawa and Okubo (2008).

ENVIRONMENTAL MANAGEMENT POLICY 1059

In our analysis, we focus on the last channel, because Felder and Rutherford (1993) andBoringer et al. (2010) argue that the changes in fuel price dominate in the source of interna-tional carbon leakage. We build a model with one fuel-producing (or fuel-exporting) countryand two fuel-consuming (or fuel-importing) countries. In the fuel-consuming countries, thenontradable sector emits GHG and causes global warming.6 We consider a two-stage policychoice game in which both fuel-consuming countries independently choose their emission regu-lation instrument, either emission taxes or emission quotas, and then, in the second stage, afterobserving which emission regulation instrument the other country has chosen, determine thespecific level of the policy instrument chosen in the first stage.

Depending on the instrument choices, different policy game equilibria emerge. When bothcountries choose emission taxes (emission quotas), the second-stage subgame is the tax–taxpolicy game (the quota–quota policy game). When one country chooses emission taxes andthe other emission quotas, the resulting second-stage game is the tax–quota policy game. Weexamine which combination of instruments emerges as a subgame perfect Nash equilibriumfor our full game and obtain three possible pure-strategy equilibria: (i) both countries alwayschoose emission quotas; (ii) one country always chooses emission quotas and, given this, theother chooses emission taxes; (iii) neither country has fixed preferences for policy instruments,but each wants to choose the different instruments from the other’s choice.

Our policy choice game captures an important aspect of the current situation of climatepolicy in the world, that is, the Durban Platform. Under the platform, all major GHG emittersare required to prepare some measures to control emissions. However, the target levels arestill highly controversial, and, hence, governments have noncooporatively determined whatkinds and levels of measures they employ.7 Our analysis yields interesting arguments as towhy adopted policy instruments could be different among countries. In particular, our resultsuggests a reason why developing countries such as China and India tend to employ emissiontaxes, whereas developed countries such as the EU tend to adopt emission quotas.8

There are many papers that compare various environmental policies including emission taxesand quotas (see, e.g., Ulph, 1996; Xepapadeas, 1997; Ishikawa and Kiyono, 2006; Lahiri and Ono,2007; Ishikawa and Okubo, 2008). Some of them argue what policy instruments should be used.To our knowledge, however, no study has rigorously examined the endogenous environmental-policy choices as a result of a policy game between countries. We explore the subgame perfectequilibrium when the countries commit to either taxes or quotas before determining specificinstrument levels.

The rest of the article is organized as follows. In Section 2, we construct a model of twofuel-consuming countries emitting GHG and one fuel-producing country and show that therelative difference in the emission coefficient, that is, the GHG emission per unit of fossil fuel,between the fuel-consuming countries determines the size of the carbon-leakage effect. Wediscuss the properties of the equilibria when the two fuel-consuming countries choose emissiontaxes in Section 3 and those when the two fuel-consuming countries choose emission quotas inSection 4. In Section 5, we discuss the unilateral equivalence between emission taxes and quotasand then the strategic nonequivalence between emission taxes and quotas. In Section 6, we ex-plore each country’s incentive to choose an environment regulation instrument within a frame-work of a two-stage policy choice game and find subgame-perfect Nash equilibria. Section 7concludes.

6 Power generation and heat supply the major source of GHG emissions. According to the International EnergyAgency (IEA), the shares of world CO2 emissions from fuel combustion for electricity and heat, transport, and industrywere, respectively, 41%, 23%, and 20% in 2007. Thus, the GHG-emission share of the nontradable is fairly high.

7 Moreover, the Kyoto Protocol was provisionally extended in COP 17. Canada and Japan were against the extensionand announced their secession from the protocol.

8 China and India are also large emitters. China was the largest CO2 emitter in 2011. Its share in the world is 27.1%.The second and the third largest emitters (as a single country) are the United States (15.9%) and India (5.5%).


2. MODEL

Consider a world consisting of three countries, with countries 1 and 2 both consuming thefossil fuel supplied by the third country, s. The economy of each country is characterized byperfect competition. Each of the fuel-consuming countries produces two goods: a homogeneoustradable commodity (other than the fossil fuel) produced only by labor and a nontradableproduced by labor, fossil fuel, and environment resources. Production of each good is subject toconstant returns to scale, and the nontradable sector requires the use of a certain combination offossil fuel and the environment. The use of fossil fuel results in GHG emissions, which degradeglobal environmental quality.

In this article, the volume of the GHG emissions is represented by the environment as an inputfactor. Thus, the tradable good is what we may call a “clean” good and the nontradable gooda “dirty” one. We refer to either of the fuel-consuming countries by superscripts i, j, k ∈ {1, 2},where i and j ( �= i) represent the different countries and k represents either one. The thirdcountry, s, a single country supplying the fossil fuel, produces the fossil fuel and the homogeneoustradable commodity.

Thus, each of the fuel-consuming countries produces and exports the tradable commodityto the fuel-supplying country and imports fossil fuel to produce the nontradable good.9 Thegovernment of neither of the three countries directly intervenes in the trade in the commodityor the fossil fuel. Hereafter, we use the nonfuel tradable good as the numeraire. The constant-returns-to-scale production technology used to produce it means that we can choose the unitsof output and input so that one unit of the tradable needs one unit of labor. This means that thewage rate should be equal to unity across the world.

As our benchmark, we construct a model in which both fuel-consuming countries regulatetheir GHG emissions by means of emission taxes.

2.1. Fuel-Consuming Country.

2.1.1. Supply-side. We start with the supply side. In a fossil fuel-consuming country, pro-duction of the dirty nontradable good emits GHG and worsens the quality of the global envi-ronment, hurting the welfare of households across the world. According to Meade (1952), theemitted GHG is an “unpaid factor of production,”pricing of which is made by the governmentin the country having the dirty industry. The specific emission tax rate on GHG serves as thefactor price of the environmental resource for firms in the dirty nontradable sector.10

Next, let r denote the world price of the fossil fuel, ti the emission tax rate set by thegovernment in fuel-consuming country i ∈ {1, 2}, and ci(r, ti) the unit cost function for the dirtynontradable sector in country i ∈ {1, 2}. We should note that the wage rage, being always unity, issuppressed in the unit cost function. The assumption of perfect competition subject to constantreturns to scale means that the equilibrium holds only when the price of the nontradable denotedby pi is equal to the unit cost, that is,

pi = ci(r, ti).

Hereafter, we assume that the unit cost function ci(r, ti) satisfies all the standard assumptionsexcept perfect complementarity between the fuel and the GHG emissions in the sense thatthere exists a certain value ei (> 0) such that

cit(r, ti) = eici

r(r, ti)(1)

9 The tradable commodity may be a composite good. If this is the case, the fossil-fuel-consuming countries may tradewith each other. This would not affect our analysis at all.

10 See also Copeland and Taylor (1994). Only one country may levy an emission tax (i.e., ti > 0 and tj = 0 (i ∈ {1, 2}and i �= j)). In this case, we can simply set tj = 0 in the following analysis of this section.


for ∀(r, ti), where cit(r, ti)

def= ∂ci(r, ti)/∂ti and cir(r, ti)

def= ∂ci(r, ti)/∂r. We call this ei the emissioncoefficient of country i ∈ {1, 2}.

One should also note that, by virtue of Shephard’s lemma, cir(r, ti) gives the input of fossil fuel

required per unit of the nontradable good, and cit(r, ti) is the counterpart for the GHG emissions

in the dirty nontradable sector. Note that this assumption of complementarity (1) leads to

citt = eici

rt < 0,

where use was made of the strict concavity of the unit cost function with respect to the fuelprice.

Next, let xi represent the output of the nontradable. Then, we may express the fossil fueldemand denoted by f i and the GHG emissions denoted by zi as follows:

f i = cir(r, ti)xi,

zi = cit(r, ti)xi = eif i.

2.1.2. Demand-side. Let us now consider the demand side. The utility of a representativeconsumer is given by

ui(xci ) + yc

i − θiD(zW ),

where xci denotes the consumption of the nontradable, yc

i the consumption of the tradable,

zWdef= ∑

k zk world total GHG emissions, D(zW ) the world damage from global warming interms of the numeraire good, and θi (> 0) what extent country i perceives this damage to be adamage to its own environment. We assume D′(zW ) > 0 and D′′(zW ) > 0. We also assume thatthe labor endowment is sufficiently large and hence yc

i > 0 holds in equilibrium.The consumer maximizes the above utility given world total GHG emissions subject to the

budget constraint

mi = pixci + yc

i ,

where mi denotes the national income and pi the domestic price of the nontradable good incountry i ∈ {1, 2}. Since there arise no excess profits in either sector, the national income is thesum of labor income and emission tax revenue, that is,

mi = Li + tizi,

where Li denotes the labor endowment of country i and use was made of the wage rate beingequal to unity.

Further, assume that the utility function ui(xci ) satisfies all the standard assumptions as well

as

limx→0

uix(x) = +∞, and lim

x→+∞ uix(x) = 0,

which assures production of the nontradable good to be always strictly positive in each country.Then, one may define the indirect utility function as follows:

vi(pi) + Li + tizi − θiD

(∑k

zk

),


where vi(pi)def= maxx{ui(x) − pixi}. In the analysis that follows, we also make use of the relation

xi(pi)def= arg maxx {ui(x) − pixi}. Finally, it should be noted that vi′(pi) = −xi(pi) holds by Roy’s

identity.

2.1.3. National welfare. To sum up, suppressing the labor endowment term, which isconstant, in the above equation, we employ the following expression for the welfare ofcountry i:

wi(r, ti)def= vi(pi) + tizi − θiD

(∑k

zk

)(2)

subject to

vi′(pi) = −xi(pi),(3)

pi = ci(r, ti),(4)

f i = f i(r, ti)def= ci

r(r, ti)xi(ci(r, ti)),(5)

zi = zi(r, ti)def= ci

t(r, ti)xi(ci(r, ti)) = eif i(r, ti).(6)

Differentiation of (2) yields

∂wi/∂ti = (ti − θiD′)zit,

∂wi/∂r = (ti − θiD′)zir −

(f i + θiD′zj

r

),

∂wi/∂tj = −θiD′zjt .

(7)

One should also note the following relations for the succeeding discussion

f ir

def= ∂f i/∂r = cirrxi + (ci

r)2xi

p < 0, f it

def= ∂f i/∂ti = eif ir,

zir

def= ∂zi/∂r = eif ir < 0, zi

tdef= ∂zi/∂ti = eif i

t = eizir < 0,

(8)

by virtue of the technological complementarity between fossil fuel and GHG. As the thirdand fourth equations of (8) show, each country’s GHG emissions decrease as the fuel priceor the emission tax rate increases, which is the source of carbon leakage considered in ouranalysis.

2.2. Fuel-Supplying Country. As in the fuel-consuming countries, the wage rate in the fuel-supplying country is equal to unity. For the purpose of focusing on the effects of fossil fuel tradeand carbon leakage, we assume that production of fossil fuel is subject to decreasing returnsto scale, though the other commodities are subject to constant returns to scale. By letting �(r)represent the maximum profit function of the fossil-fuel sector, Hotelling’s lemma implies that�′(r) gives the supply function of the fossil fuel, which we represent by s(r).


2.3. World Trade Equilibrium. To express the equilibrium, it suffices to write down theworld fossil fuel market clearing condition, that is,

s(r) −∑

j

f j (r, ti) = 0.(9)

Given the emission tax policies of the fuel-consuming countries t def= (t1, t2), the world fuelprice is determined via (9), the relation of which we express by r(t). When either fuel-consuming country raises the emission tax rate, this dampens its fuel demand, thus leadingto a decline in the equilibrium fuel price. To show this effect on the price, we define thefollowing:

�rdef= s′(r) −

∑k

f kr (> 0),(10)

ζ�def=

{ −f ir/�r for � ∈ {1, 2}

s′(r)/�r for � = s.(11)

Here, ζi represent the relative price sensitivity of fuel demand by country i ∈ {1, 2} and ζs therelative price sensitivity of fuel supply by the fuel-supplying country. By definition, the followingholds:

ζ� ∈ (0, 1),∑

�

ζ� = 1 for � ∈ {1, 2, s}(12)

In terms of these relative price sensitivities, one can express the effect of an increase infuel-country i’s emission tax rate on the fuel price as follows:

ri(t)def= ∂r/∂ti = −eiζi < 0,(13)

where use was made of (8). The following lemma is straightforward from (13).

LEMMA 1. (i) The world fuel price always declines as one of the fuel-consuming countriesraises its emission tax rate. (ii) The decrease in the world fuel price caused by an increase in afuel-consuming country’s emission tax rate becomes greater as its emission coefficient and relativeprice sensitivity of fuel demand increase.

Note that, with fuel-consuming countries facing an upward-sloping fuel-supply functions′(r) > 0, the above lemma critically depends on the market power of each fuel-consumingcountry. If country i is small with no market power in the world fuel market, then it cannotaffect the world fuel price.

2.4. Emission Taxes and GHG Emissions. Before investigating each country’s strategic in-centive for environment regulation, let us look into the effects of emission tax increases onGHG emissions, which are the key to the following analysis.

For this purpose, we first redefine the demand for fuel and GHG emissions as a function ofthe emission tax rates of the two countries, that is, the emission-tax profile t = (t1, t2):

f i(t) def= f i (r(t), ti) , zi(t) def= zi (r(t), ti) .(14)


These input demand functions satisfy

f ii

def= ∂f i(t)/∂ti = f it + f i

r ri = −�rei(1 − ζi)ζi < 0,

f ij

def= ∂f i(t)/∂tj = f ir rj = �rejζiζj > 0,

zii

def= ∂zi(t)/∂ti = eif ii = −�re2

i ζi(1 − ζi) < 0,

zij

def= ∂zi(t)/∂tj = eif ij = �reiejζjζi = zj

i > 0,

(15)

where use was made of (8). The above equations show that an increase in the emission tax rateby a fuel-consuming country decreases its own fuel demand as well as its own GHG emissions,whereas it increases those of the other fuel-consuming country (only when there is a decreasein the world fuel price).

An increase in the emission tax by one country lowers the fuel price, leading to an increasein the fuel demand of the other country and hence an increase in its GHG emissions. This isthe basic mechanism of carbon leakage via trade in fuel considered in this study. This carbon-leakage effect involves the possibility of an increase in world total GHG emissions even withan increase in the emission tax rate of one of the countries.

To show this possibility of an increase in world total GHG emissions, let

zW (t) def=∑

k

zk(t), f W (t) def=∑

k

f k(t),

respectively, represent world total GHG emissions and fuel demand as a function of the taxprofile. Using (13) and (15), the effect of an increase in ti (i = 1, 2) on world total GHG emissionsand fuel demand can be represented as

f Wi

def= ∂f W (t)/∂ti = s′(r)ri = −s′(r)eiζi < 0,(16)

zWi

def= ∂zW (t)/∂ti = �reiζi{ejζj − ei(1 − ζi)},

the latter of which can also be rewritten as

zWi = �reiej (1 − ζi)ζi

{ζj

1 − ζi− ei

ej

}.(17)

Thus, an increase in the emission tax by either of the two countries unambiguously reducesthe world fuel demand (see (16)), but, as (17) shows, it may increase world total GHG emissions.

PROPOSITION 1. Suppose that country i ∈ {1, 2} raises its emission tax rate. Then, world totalGHG emissions decrease if and only if ei/ej > ζj/(1 − ζi).

Hereafter, without loss of generality, we assume that the emission coefficient is not larger incountry 1 than in country 2, that is, e1 ≤ e2.11 Then, there are two possible cases when discussingthe change in world total GHG emissions through an increase in either country’s emission taxrate. They are illustrated in Figure 1.

11 e1 < e2 could stem from differences in artificial carbon sinks between countries. Artificial carbon sinks called“carbon capture and storage (CCS)” mitigate the carbon dioxide release into the atmosphere from fossil fuel use.According to the IEA, CCS is the only technology available to mitigate GHG emissions from large-scale fossil fuelusage. In IEA’s scenario, CCS will contribute to 20% reductions of GHG emissions in 2050. Since developed countriessuch as Japan and Germany have been developing CCS technologies, the emission coefficient is expected to be lowerin developed countries than in developing countries.


FIGURE 1

CHANGES IN EMISSION TAXES AND WORLD TOTAL GHG EMISSIONS

When the emission coefficients of the two fuel-consuming countries do not differ to a greatextent and hence the relative emission coefficient e1/e2 is in Region N (i.e., ζ2/(1 − ζ1) <

e1/e2 ≤ 1), an increase in either country’s emission tax rate decreases world total GHGemissions.12 If the emission coefficients differ a lot and hence e1/e2 is in Region A (i.e.,0 < e1/e2 < ζ2/(1 − ζ1)), however, an increase in the emission tax rate by country 1 increasesworld total GHG emissions. This is because, provided the emission coefficient of country 1 issufficiently smaller than that of country 2, such a tax increase lowers the fuel demand and thusGHG emission by country 1 with the smaller emission coefficient but the resulting decrease inthe fuel price boosts the fuel demand by country 2 with the larger emission coefficient, leadingto a large increase in GHG emissions.

Given ζs, a decrease in ζ1 (a relative price sensitivity of fuel demand by country 1), which isequivalent to an increase in ζ2 (see (12)), expands Region A. A small ζ1 or a large ζ2 impliesthat a change in country 1’s fuel demand caused by a given price change is small, and a changein country 2’s fuel demand caused by a given price change is large. For example, this is likelyto be the case when country 1 is relatively small and/or has a relatively small price elasticityof demand.13 As ζ1 becomes smaller, the above-mentioned carbon-leakage effect is magnified,and, hence, world total GHG emissions are more likely to increase.

As already mentioned, the possibility of an increase in world GHG emissions as a result of anincrease in the emission tax in a country depends on the country’s market power in the worldfuel market. In fact, when the fuel price is constant, the increase in a country’s emission taxrate only affects its own GHG emissions, so that in this case world total GHG emissions alwaysdecrease.

We should mention that the zW1 + zW

2 < 0 holds.14 Therefore, even when an increase in theemission tax by country 1 with the smaller emission coefficient increases world total GHGemissions, the following lemma is established.

LEMMA 2. When both fuel-consuming countries simultaneously raise their emission tax ratesby the same amount, there must be a decrease in world total GHG emissions.

3. THE INDIVIDUALLY OPTIMAL EMISSION TAX

Our next task is to explore the properties of the equilibria when the two fuel-consumingcountries noncooperatively choose optimal emission taxes and/or quotas. In this section, welook at the case in which each fuel-consuming country sets its emission tax rate knowing the

12 If countries 1 and 2 are symmetric and hence e1 = e2 and ζ1 = ζ2 hold, then we have ζ2/(1 − ζ1) < e1/e2 = 1because ζ1 = ζ2 < 1/2 holds from (12).

13 If the two countries have the identical price elasticity of demand, ζ1 < ζ2 implies that country 1 is smaller thancountry 2. If the country sizes are identical, on the other hand, ζ1 < ζ2 implies that country 1 has a smaller price elasticityof demand than country 2.

14 The proof is provided in Appendix A.1.


other country also employs emission taxes, which we call the tax–tax policy equilibrium. Sincethe optimal tax rate should maximize each country’s national welfare given the other’s tax rate,we refer to it as the individually optimal emission tax rate in the following discussion.

3.1. Determinants of the Optimal Emission Tax. In this subsection, we point out that thereare three determinants of the individually optimal emission tax rate. For this, we obtain theindividually optimal emission tax rate. Inserting the equilibrium fuel-price function into (2), wecan express each country’s welfare as the following function of the tax profile:

wiT (t) def= wi (ti, r(t)) .(18)

We assume that the above welfare function is strictly concave in the country’s own emission taxrate.

Since the optimal tax rate is chosen noncooperatively, it should satisfy the following first-ordercondition for welfare maximization:

0 = ∂wiT

∂ti= ∂wi

∂ti+ ∂wi

∂rri

= (ti − θiD′)zit +

{(ti − θiD′)zi

r − (f i + θiD′zjr)}

ri

= (ti − θiD′)zii − f iri − θiD′zj

r ri,

(19)

where use was made of (7). Letting tTi represent the solution of the above first-order condition

for welfare maximization, that is, country i’s emission tax rate at the noncooperative tax–taxpolicy game equilibrium, we have

tTi = θiD′ + f i

(ri

zii

)+ θiD′

(zj

i

zii

),(20)

or, alternatively,

tTi = f i

(ri

zii

)+ θiD′

(zW

i

zii

)(21)

= f i

�rei(1 − ζi)+(

1 − ejζj

ei(1 − ζi)

)θiD′,(22)

where use was made of (13) and (15).In (20), each term represents different determinant of emission tax.15 The first term represents

the well-known basic motive for internalizing negative externalities caused by emissions. Thisterm is obviously positive. The second term is related to the terms of trade (TOT) for fuel.As a result of an emission tax, the fuel-consuming country can improve the TOT for fuel andhence welfare. This effect works to raise the emission tax rate. Finally, the last term arisesbecause of carbon leakage. Since an increase in the emission tax rate lowers the fuel price,the other fuel-consuming country’s demand for the fossil fuel is boosted, which worsens theglobal environment quality through an increase in GHG emissions. This carbon-leakage effectworks to reduce the emission tax rate. If this carbon-leakage effect is sufficiently large, then

15 This decomposition is similar to that in Markusen (1975) who investigates tariffs, consumption taxes, and productiontaxes in the presence of international externalities in a two-country model.


the optimal policy would in fact be to impose a negative, instead of a positive, emission taxrate. This case occurs only when an increase in the emission tax rate increases world total GHGemissions (i.e., zW

i > 0), as is shown in (21). Since zW2 < 0 always holds with e1 ≤ e2, the optimal

emission tax could be negative only in country 1.Therefore, we obtain the following proposition.

PROPOSITION 2.

(1) Given the emission tax rate of the other country, the TOT effect makes the optimal emissiontax rate for a fuel-consuming country higher, but the carbon-leakage effect makes it lower.

(2) Given the emission tax rate of the other country, each fuel-consuming country sets a strictlypositive rate of emission tax if an increase in its own emission tax rate decreases world totalGHG emissions. A negative emission tax rate is optimal only in country 1. This is the caseonly if an increase in country 1’s emission tax rate increases world total GHG emissions.

Note that the carbon-leakage effect vanishes when a fuel-consuming country is a price takerin the world fuel market, so that its optimal emission tax rate is given by

tTi = θiD′

(∑k

zk

).(23)

The emission tax rate should be set equal to the perceived marginal environment damage. Thisresult is the same with the standard result obtained in a closed-economy model where neitherthe TOT effect nor the carbon-leakage effect exists.

We should mention that the effect of an increase in the emission coefficient on the optimalemission tax rate is ambiguous. It increases the marginal environment damage, D′. It is straight-forward from (23) that an increase in D′ induces the country to raise the optimal emission taxrate without carbon leakage. However, this is not necessarily the case with carbon leakage (see(21)). That is, an increase in country i’s emission coefficient raises country i’s optimal emissiontax rate without carbon leakage, but may lower it with carbon leakage.

3.2. Shapes of the Reaction Curves. When we solve (19) for the own emission tax rate, thesolution gives country i’s reaction function, which we denote by RiT (tj ). In this subsection, wediscuss its shape.

As has been made clear in the previous literature, when each fuel-consuming country is aprice taker in the world fuel market, the optimal emission tax rate formula (23) implies thatthe optimal emission tax of one country decreases as that of the other country increases. Thisis because an emission tax increase by the other country decreases the own GHG emissionsas well as the world total, which decreases the marginal environment damage. This leads thefirst country to lower its emission tax rate. For this reason, each country’s reaction curve isdownward-sloping in the tax–tax policy game in the absence of the carbon-leakage effect.

However, as is implied by (20), once the carbon-leakage effect occurs, the shape of thereaction function may change, and it is possible that it becomes upward-sloping.

LEMMA 3. In the presence of carbon leakage through fuel trade, each country’s emission taxrate is not necessarily a strategic substitute to the other’s tax rate in the tax–tax policy game.

3.3. Changes in the Marginal Environment Consciousness. It may be of interest to examinehow each country’s optimal emission tax rate changes along with the marginal environmentconsciousness, θi. We can easily find the effect of a change in the marginal environment con-sciousness, because it does not affect the fuel demand or the GHG emissions of either country.


Partial differentiation of (19) yields

∂2wiT

∂θi∂ti= −D′zW

i ,

where use was made of the envelope theorem, zWi = zi

i + zji and zj

i = zjr ri.

Thus, we establish the following proposition.

PROPOSITION 3. When country i ∈ {1, 2} becomes more environment conscious in the sense thatθi increases, its optimal emission tax rate increases if and only if an increase in country i’s emissiontax rate decreases world total GHG emissions.

In view of Proposition 1, an increase in θ2 necessarily raises country 2’s optimal emission taxrate, whereas an increase in θ1 may lower country 1’s optimal emission tax rate. As is clear from(23), an increase in θi necessarily raises country i’s optimal emission tax rate without carbonleakage. This relationship holds even with carbon leakage, however, as long as the leakage isnot strong enough.

3.4. A Tax Increase by the Other Country. We next consider whether a fuel-consumingcountry gains or loses if the other fuel-consuming country raises its emission tax rate. Specifically,we evaluate this effect when the country initially employs the optimal-response emission taxrate.

It is proved in Appendix A.2 that even in the presence of carbon leakage, one finds that atax increase by either fuel-consuming country benefits the other country. That is, ∂wiT /∂tj > 0holds.

PROPOSITION 4. Given the individually optimal emission tax rate, the welfare of either of thefuel-consuming countries improves as the other country increases the emission tax rate.

Thus, as in the standard literature, emission taxation by a fuel-consuming country gives riseto pecuniary external economies to the other fuel-consuming country. Using this result, it isstraightforward to depict each country’s iso-welfare contour at the noncooperative equilibrium,as shown in Figure 2. In the figure, point T1 is the noncooperative equilibrium. Country i’sisowelfare contour is given by wT

i . Thus, the two fuel-consuming countries are better off byraising their tax rates above those at the noncooperative equilibrium. Note that this result holdsregardless of whether the emission tax rates are strategic substitutes or complements.

4. THE INDIVIDUALLY OPTIMAL EMISSION QUOTA

In this section, we examine the case in which both fuel-consuming countries employ emissionquotas. By emission quota, we mean a countrywide cap of total GHG emissions. We assume thatthe government issues a certain number of GHG emission permits and establishes a perfectlycompetitive market for the domestic trade in such permits.

4.1. The Optimal Emission Quota. Consider a policy game in which both fuel-consumingcountries employ emission quotas. We call this the quota–quota policy game. Let qi denote

country i’s quota and q def= (q1, q2) the quota profile. In view of (2)–(6), each fuel-consumingcountry’s welfare is now described by

wiQ(ti, r) def= vi(pi) + tiqi − θiD

(∑k

qk

)(24)


FIGURE 2

JOINTLY BETTER TAX PROFILES FOR THE FUEL-CONSUMING COUNTRIES

subject to

vi′(pi) = −xi(pi),(3)

pi = ci(r, ti),(4)

f i = f i(r, ti),(5)

qi = zi(r, ti) = eif i(r, ti),(25)

s(r) =∑

i

qi

ei,(26)

where ti now represents the price of the tradable emission permit in country i. The last equation,(26), determines the equilibrium fuel price as a function of the quota profile, which we expressby rQ(q). Simple calculation yields

∂rQ(q)∂qi

= 1eis′(r)

> 0,

which implies

LEMMA 4. The world fuel price always declines as one of the fuel-consuming countries decreasesthe level of its emission quota.


We insert rQ(q) into (25), and solve for ti. We then obtain the price of the tradable permit asa function of the quota profile, which we express by ti(q). From rQ(q) and ti(q), the country’swelfare is represented as a function of the quota profile:

wiQ(q) def= wiQ(ti(q), rQ(q)).

In the quota–quota policy game, each country sets the quota so as to maximize its welfare givenby (24), so that the following first-order condition holds:

0 = ∂wiQ

∂qi= (− xici

t + qi) ∂ti(q)

∂qi+ (− xici

r

) ∂rQ(q)∂qi

+ (ti − θiD′)

= − f i

eis′(r)+ (ti − θiD′) ,

(27)

where use was made of (25) and f i = cirxi.

Solving the above equation for the permit price, we obtain

tQi = θiD′ + f i

eis′(r),(28)

which, compared with (20), shows that there are no carbon-leakage effects. This means thateach fuel-consuming country has an incentive to strengthen its environmental regulation bysetting a higher price for emission permits.

The following proposition is established.

PROPOSITION 5. If both fuel-consuming countries employ emission quotas, then there are nocarbon-leakage effects, and hence each country has an incentive to strengthen its environmentalregulation compared with the case of emission taxes.

4.2. Reaction Curves in the Quota–Quota Policy Game. In this subsection, we explore re-action curves in the quota–quota policy game. In general, the shape of the associated reactioncurve is ambiguous. In the absence of fuel trade, (28) is rewritten as tQ

i = θiD′. Since the do-mestic permit price is independent of the other country’s quota, it is straightforward to see thateach country’s emission quota is a strategic substitute to the other’s. In the presence of fueltrade, however, this is not necessarily the case.

Let us now examine the relationship between the original reaction functions in terms ofemission quota levels and the corresponding reaction curve in terms of the price of the tradableemission permit. The transformed reaction curves below allow us to make comparisons amongthe equilibria in different games.

Let �i(qj )def= arg maxqi w

iQ(q). Since qk = zk(t) holds for k ∈ {1, 2}, the reaction function interms of the permit price, ti = RiQ(tj ), should satisfy

zi(t) = �i(zj (t)).

Thus, the transformed reaction function, RiQ(tj ), should satisfy

dRiQ(tj )dtj

=d�i(qj )

dqjzj

j − zij

zii − d�i(qj )

dqjzj

i

.


Since

zii

zji

= −ej (1 − ζi)eiζj

(29)

holds by virtue of (15), we can rewrite the slope of the transformed reaction function as follows:

dRiQ(tj )dtj

= − zjj

zji

d�i(qj )dqj

+ ej (1−ζj )eiζi

d�i(qj )dqj

+ ej ζj

ei(1−ζi)

.

Since ejζj/ei(1 − ζi) < ej (1 − ζj )/eiζi always holds, it is straightforward to obtain the followinglemma from the above equation:

LEMMA 5.

dRiQ(tj )dtj

< 0 ⇐⇒

⎧⎪⎪⎪⎨⎪⎪⎪⎩(i)

d�i(qj )dqj

< 0,

(ii)ejζj

ei(1 − ζi)<

∣∣∣∣d�i(qj )dqj

∣∣∣∣ <ej (1 − ζj )

eiζi.

As the above lemma shows, under the quota–quota policy game, the reaction curve in terms ofthe price of the tradable emission permit becomes upward-sloping even when the correspond-ing reaction curve in terms of emission quota levels is downward-sloping. When the originalreaction curve in the quota–quota policy game over the quota–quota space is upward-sloping,the corresponding transformed reaction curve should always be upward-sloping.

4.3. A Quota Decrease by the Other Country. What if the other country reduces its emissionquota level in the quota–quota policy game? The following shows that if a country optimizes itsemission quota in response to the quota set by the other country, such a decrease in the othercountry’s quote unambiguously improves the welfare of the first country:

dwiQ(�i(qj ), qj

)dqj

= ∂wiQ(�i(qj ), qj

)∂qj

(by virtue of the envelope theorem)

= −θiD′ − f irQj < 0.(30)

Thus, in the quota–quota policy game, each country’s choice of the emission quota levelgenerates external diseconomies for the other country. This means that the incentive for eachcountry to reduce GHG emissions through quotas is not enough from the viewpoint of the jointwelfare of both fuel-consuming countries.

Thus, we have established

PROPOSITION 6. If both fuel-consuming countries further reduce their GHG emissions throughquotas, then both can be better off than at the noncooperative quota–quota policy game equilib-rium.

5. THE EQUIVALENCE BETWEEN TAXES AND QUOTAS

Depending on the instrument choices, different policy game equilibria emerge. When bothcountries choose emission taxes (emission quotas), the second-stage subgame is the tax–tax


policy game (the quota–quota policy game). When one country chooses emission taxes andthe other emission quotas, the resulting second-stage game is the tax–quota policy game. Wecompare the equilibria with the aid of reaction curves depicted over the t1–t2 space. Bothunilateral equivalence and strategic nonequivalence below are useful when investigating reactioncurves.

5.1. Unilateral Equivalence. From the viewpoint of an individual country, taxes and quotas,given the policy instrument of the other country, can be shown to be equivalent in the sensethat they achieve the same world resource allocation. We call this result unilateral equivalencebetween emission taxes and quotas.16

First, suppose that country j employs emission taxes. Then in view of (14), given country i’semission quota qi, the equilibrium permit price ti should satisfy

qi = zi(ti, tj ).

Thus, given country j ’s emission tax rate, there is a one-to-one relationship between the emissionquota qi and the emission tax rate or permit price ti. This establishes that emission taxes andquotas are equivalent for country i given country j ’s emission tax rate.

Next consider the case in which country j sets the emission quota qj . Then, given qj , whencountry i chooses the emission quota qi, the resulting permit prices, ti and tj , should satisfy

qi = zi(ti, tj ), qj = zj (tj , ti).

Since

�zdef= z1

1z22 − z1

2z21 > 0(31)

holds,17 the implicit function theorem can be applied to ensure a one-to-one relationship be-

tween the permit-price profile t and the emission-quota profile q def= (q1, q2). This implies thatemission taxes and quotas are equivalent for country i given country j ’s emission quota.18 Theabove discussion leads to the following unilateral equivalence result.

PROPOSITION 7. Given the environmental policy instrument of the other fuel-consuming country,emission taxes and quotas are equivalent for each individual country.

This proposition implies the following lemma.

LEMMA 6. Given the other country’s environmental policy instrument, a country’s reactioncurves are the same regardless of its choice between taxes and quotas once they are transformedand depicted over the t1–t2 space.

In Figure 3, RiT is country i’s reaction curve given that country j employs emission tax. ti is thetax rate (the permit price) in country i when country i employs emission tax (quota). Similarly,RiQ is country i’s reaction curve given that country j employs emission quota.19

16 This is similar to the well-known tax–quota equivalence in a closed economy.17 This result is obtained as follows:

�z = (z1t + z1

r r1)(z2t + z2

r r2) − z1r z2

r r1 r2 = z1t z2

t + z1t z2

r r2 + z1r z2

t r1 = e1e2(f 1t f 2

t + f 1t f 2

r r2 + f 1r f 2

t r1) = e21e2

2f 1r f 2

r ζs > 0.

18 A more rigorous proof is provided in Appendix A.3.19 As shown in Lemma 7 below, RiQ is located outside of RiT .


FIGURE 3

(a) REACTION CURVES: THE CASE OF STRATEGIC SUBSTITUTES. (b) REACTION CURVES: THE CASE OF STRATEGIC COMPLEMENTS

5.2. Strategic Nonequivalence. Even when emission taxes and quotas are equivalent giventhe other country’s environmental policy instrument, they are no longer equivalent once theother country changes its policy instrument. In fact, once the other country switches fromemission taxes to quotas, each country has an incentive to strengthen its own environmentalregulation. Let us demonstrate this result, which we call the strategic nonequivalence result.

We assume that the two countries initially employ emission taxes. In Figure 2, the equilibriumis given by point T1 where the reaction curves (which are not shown in the figure to avoid itgetting too complex) intersect with each other. Now suppose that country 2 switches fromemission taxes to quotas. Given the associated tax profile, draw a curve showing the tax pairskeeping country 2’s GHG emissions constant. This iso-GHG-emissions curve is given by zT

2 zT ′2 .

In view of (15), such a curve should be upward-sloping. Then, since country 1’s isowelfarecontours are U-shaped as shown in Figure 2 and its welfare improves in the higher country2’s emission tax rate, country 1 becomes better off by choosing point Q1 along the iso-GHG-emissions curve zT

2 zT ′2 .

The result is that country 1’s emission tax rate becomes higher as well as country 2’s. Thereason is as follows. Since country 2’s GHG emissions are held constant, its fuel demand is also


kept constant under the emission quota. This implies that country 1’s tax increase results in nocarbon leakage, leading to an increase in the emission tax rate.

How do the GHG emissions by country 1 change after such a change in the emission taxpolicy? The figure also shows the iso-GHG-emissions curves for country 1, zT

1 zT ′1 and zQ

1 zQ′1 .

They are also upward-sloping and their slopes are greater than country 2’s by virtue of thefollowing relation

dt2dt1

∣∣∣∣z1=const

− dt2dt1

∣∣∣∣z2=const

= z21

z22

− z11

z12

= 1

z22z1

2

(z1

2z21 − z1

1z22

)> 0,

where use was made of (31).Since z1

1 < 0, GHG emissions on the iso-GHG-emissions curve zQ1 zQ′

1 are smaller than thoseon the curve zT

1 zT ′1 . This is consistent with the result for the case above when country 1 employs

more stringent environmental regulations.Thus, we obtain

PROPOSITION 8. If a country switches from an emission tax to an individually equivalentemission quota, then the other country has an incentive to raise its emission tax rate or to reduceits emission quota level.

Thus, environmental quotas are a more stringent policy instrument than environmental taxesin the sense that environmental quotas lead the other country to strengthen environmentalregulations in the other country in the presence of carbon leakage. The above proposition alsoimplies that when one country switches from an emission tax to a quota, the other country’sreaction curve (which is not shown in Figure 2 but in Figure 3) shifts outside on the t1–t2 plane.20

That is,

LEMMA 7. Country i’s reaction curve given that country j employs emission quota is locatedoutside of country i’s reaction curve given that country j employs emission tax.

We should mention that below (above) the iso-GHG-emissions curve zT2 zT ′

2 , country 2’s GHGemissions are larger (smaller) than at T1. Similarly, above (below) the iso-GHG-emissions curvezT

1 zT ′1 , country 1’s GHG emissions are larger (smaller) than at T1. Thus, the world iso-GHG-

emissions curve which keeps world total GHG emissions at the level of T1 goes through theregions zT

1 T1zT ′2 and zT ′

1 T1zT2 . The world iso-GHG-emissions curve is downward-sloping in Case

N of zW1 < 0 and zW

2 < 0 (i.e., when e1/e2 lies in Region N in Figure 1) but is upward-sloping inCase A of zW

1 > 0 and zW2 < 0 (i.e., when e1/e2 lies in Region A in Figure 1).21 Therefore, we

obtain

PROPOSITION 9. When both t1 and t2 increase, total world GHG emissions necessarily decreaseif e1/e2 > ζ2/(1 − ζ1) but could increase if e1/e2 < ζ2/(1 − ζ1).

6. STRATEGIC INTERDEPENDENCE AND SUBGAME NASH EQUILIBRIA

In this section, we find subgame perfect Nash equilibria in the following two-stage policygame. In the first stage, both fuel-consuming countries independently choose their emissionregulation instrument, either emission taxes or emission quotas, and then, in the second stage,after observing which emission regulation instrument the other country has chosen, determinethe specific level of the policy instrument chosen in the first stage.

20 The resulting new reaction curve does not necessarily have the same shape as the original curve.21 In Case A, the iso-GHG-emissions curve has a slope of less than unity by virtue of Lemma 2.


6.1. Specific Level of Policy Instruments in the Different Policy Games. The result of thestrategic nonequivalence of emission taxes and quotas implies that the quality of the globalenvironment will differ depending on each country’s choice of policy instrument. These differ-ences are shown in Figure 3. Figure 3(a) shows the case in which the reaction curves of bothfuel-consuming countries are downward-sloping, whereas Figure 3(b) shows the case in whichthey are upward-sloping.

In the figures, each intersection of the reaction curves of the two countries represents anoncooperative environmental policy equilibrium for each possible combination of instrumentchoices. Thus, for example, point ETQ shows the equilibrium when country 1 chooses emissiontaxes and country 2 emission quotas.

6.2. Welfare Comparison. As already discussed in Section 4.1, in the quota–quota policygame, both countries tend to strengthen their environmental regulation compared with thetax–tax policy game. Moreover, in view of Proposition 4, one may be tempted to conclude thatboth countries would be better off at the quota–quota policy game equilibrium EQQ than at thetax–tax policy game equilibrium ETT .

In general, however, this is not correct. The reason is that EQQ does not always lie withinthe set of the tax profiles dominating ETT for both countries. A possible case is depicted inFigure 3(b). If the welfare contours going through point ETT are given by wT

1 and wT2 , then both

countries would be better off at ETT than at EQQ. Note that from Proposition 9, although botht1 and t2 are higher at EQQ than at ETT , total world GHG emissions could be larger at EQQ thanat ETT . If e1/e2 < ζ2/(1 − ζ1) holds and EQQ is located below T1zT

W in Figure 2 (where EQQ isnot indicated), then world total GHG emissions are greater at EQQ than at T1 (i.e., ETT ).

Therefore, one may think it difficult to compare two equilibria, one or both of which areoff the reaction curve, RiT (tj ), on the t1–t2 space. However, we can derive conditions that helpus to make a welfare comparison among the possible equilibria. To derive the conditions, letus compare EQQ with the equilibrium in which country i chooses emission taxes but country jchooses emission quotas. Movement from the latter to the former requires changes in the taxprofile along country i’s transformed reaction curve RiQ(tj ) (see Figures 3a and 3b) becausecountry j employs emission quotas and does not switch its policy. When country i switches toemission quotas, country j has an incentive to alter its emission quota so as to raise the price ofdomestic emission permits or, effectively, the emission tax rate.

The associated effect on country i’s welfare is given by

dwiQ(zi(RiQ(tj ), tj ), zj (RiQ(tj ), tj ))dtj

= ∂wiQ(�i(zj (RiQ(tj ), tj )), zj (RiQ(tj ), tj ))∂qi

dzi(RiQ(tj ), tj )dtj

+ ∂wiQ(�i(zj(RiQ(tj ), tj

)), zj

(RiQ(tj ), tj

))∂qj

dzj(RiQ(tj ), tj

)dtj

= −(

f irQj + θiD′

) dzj(RiQ(tj ), tj

)dtj

(32)

= −(

f irQj + θiD′

)zj

i

{dRiQ(tj )

dtj− ej (1 − ζj )

eiζi

},(33)

where use was made of the envelope theorem (15), (29), and (30). Thus, country i is better off byswitching to emission quotas given country j ’s choice of emission quotas if and only if country j ’sGHG emissions decrease with an increase in its emission tax rate along country i’s transformedreaction curve (see (32)) or, alternatively, if and only if dRiQ(tj )/dtj < ej (1 − ζj )/eiζi (see (33)).Ceteris pairibus, a country gains from a reduction of the other country’s GHG emissions.


(32) tells us that as long as country i optimally responds to country j ’s reaction to country i’sswitch, country j ’s GHG emissions decrease makes country i better off. If country i’s transformedreaction curve, RiQ(tj ), is downward-sloping (i.e., dRiQ(tj )/dtj < 0),22 then country i ’s switchdecreases ti and increases tj , and hence country j ’s GHG emissions decrease. Thus, country i’swelfare improves. If RiQ(tj ) is upward-sloping, on the other hand, both ti and tj increase. If tirises a lot relative to tj (which arises when dRiQ(tj )/dtj is large), however, country i’s switchcould actually increase country j ’s GHG emissions,23 which worsens country i’s welfare.

Similarly, we obtain

dwjQ(zi(RiQ(tj ), tj

), zj

(RiQ(tj ), tj

))dtj

= −(

f j rQi + θj D′

) dzi(RiQ(tj ), tj

)dtj

= −(

f j rQi + θj D′

)zi

i

{dRiQ(tj )

dtj− ejζj

ei(1 − ζi)

}.

Thus, country j is better off by country i’s switch from emission taxes to emission quotas givencountry j ’s choice of emission quotas if and only if country i’s GHG emissions decrease withan increase in country j ’s emission tax rate along country i’s transformed reaction curve or,alternatively, if and only if dRiQ(tj )/dtj > ejζj/ei(1 − ζi). If RiQ(tj ) is downward-sloping, thencountry i’s switch makes country j worse off because ti falls and tj rises, and hence country i’sGHG emissions increase. If RiQ(tj ) is upward-sloping, on the other hand, both ti and tj increase.If ti increases a lot relative to tj , however, country i’s switch could decrease country i’s GHGemissions, which improves country j ’s welfare.

Let ETiQj denote the equilibrium in which country i chooses emission taxes and country jemission quotas, and EQQ i ETiQj mean that country i’s welfare is strictly higher at EQQ thanat ETiQj . Then the above discussion can be summed up in the following proposition.

PROPOSITION 10.

(1) EQQ i ETiQj if and only if country j ’s GHG emissions decrease with an increase inits emission tax rate along country i’s transformed reaction curve (i.e., dRiQ(tj )/dtj <

ej (1 − ζj )/eiζi).(2) EQQ j ETiQj if and only if country i’s GHG emissions decrease with an increase in

country j ’s emission tax rate along country i’s transformed reaction curve (i.e.,dRiQ(tj )/dtj > ejζj/ei(1 − ζi)).

The following two things should be noted. First, in Figure 3a, dRiQ(tj )/dtj < 0 < ej (1 −ζj )/eiζi holds. Thus, we obtain EQQ i ETiQj and ETiQj j EQQ. In Figure 3b, however,what we can tell with respect to the slope of reaction curve, RiQ, is just dRiQ(tj )/dtj > 0.Thus, EQQ i ETiQj may not hold. ETiQj j EQQ may not hold, either. Second, in view ofProposition 4, we can claim that on RiQ(tj ), a higher tj leads to the higher welfare of country i.Thus, EQiTj i ETT holds.

The above results are summarized in Figure 4. Noting ei(1 − ζi)/ejζj > eiζi/ej (1 − ζj ), wehave four regions in the figure. We can easily confirm in the figure that the quota–quota policygame equilibrium EQQ may not be the best for both countries.

6.3. Policy Instrument Choices. We are now ready to determine which combination of theenvironment regulation instruments emerges as a subgame perfect Nash equilibrium for ourfull game. Noting Figure 4, we can draw Figure 5, which illustrates nine regions to be examined.Appendix A.4 shows that when both countries simultaneously choose a policy instrument, EQQ

22 Note that dRiQ(tj )/dtj < 0 implies dRiQ(tj )/dtj < ej (1 − ζj )/eiζi, because ej (1 − ζj )/eiζi > 0.23 Recall that the iso-GHG-emissions curve for each country is upward-sloping as in Figure 2.


FIGURE 4

WELFARE RANKING OF POSSIBLE EQUILIBRIA FOR COUNTRY i

FIGURE 5

NASH EQUILIBRIA

arises in Regions I, II, IV, and V; EQT arises in Regions VII and VIII; ETQ arises in Regions IIIand VI; and ETQ and EQT could arise in Region IX.

The above result is summarized in Figure 6. In Region QQ, a quota policy is the dominantstrategy for both countries, so that EQQ arises. In Region QT (TQ), the choice of a quotapolicy dominates that of a tax policy for country 1 (country 2) but country 2 (country 1) prefersemission taxes when country 1 (country 2) chooses quotas, so that EQT (ETQ) arises. In RegionU, each country is better off by choosing a policy instrument different from the other’s choice,


FIGURE 6

POSSIBLE EQUILIBRIA

so that there are at least three equilibria; two are pure-strategy equilibria, ETQ and EQT , andthe last is a mixed-strategy equilibrium.24

The above result is summarized in the following proposition.

PROPOSITION 11. Both countries choose emission quotas if both dR1Q(t2)/dt2 < e2(1 − ζ2)/e1ζ1

and dR2Q(t1)/dt1 < e1(1 − ζ1)/e2ζ2 hold (i.e., in Region QQ in Figure 6). Countries 1 and 2,respectively, choose an emission tax and an emission quota if both dR1Q(t2)/dt2 > e2(1 − ζ2)/e1ζ1

and dR2Q(t1)/dt1 < e1(1 − ζ1)/e2ζ2 hold (i.e., in Region TQ) and vice versa if both dR1Q(t2)/dt2 <

e2(1 − ζ2)/e1ζ1 and dR2Q(t1)/dt1 > e1(1 − ζ1)/e2ζ2 hold (i.e., in Region QT).

This proposition suggests a reason why employed policy instruments are different acrosscountries. If both (transformed) reaction curves are downward-sloping, then both countriesnecessarily choose an emission quota. If both (transformed) reaction curves are upward-sloping,on the other hand, other combinations are also possible.

A decrease in e1/e2 expands Region QT and shrinks Region TQ. Moreover, given ζs, a decreasein ζ1 or an increase in ζ2 also expands Region QT and shrinks Region TQ. Whereas a shrinkagein Region TQ implies that country 1 is more likely to choose emission quotas, an expansion ofRegion QT implies that country 2 is more likely to choose emission taxes.

Therefore, as the countries become more asymmetric, they are more likely to employ dif-ferent environmental policies. In particular, a small e1 or a large e2 implies that country 1 hasbetter environmental technologies. Also, a small ζ1 or a large ζ2 is likely to be the case whencountry 1 is relatively small and/or has a relatively small price elasticity of demand. Thus, acountry with better environmental technologies, a smaller size, and a smaller price elasticity ofdemand is more likely to employ emission quotas, whereas a country with worse environmentaltechnologies, a larger size, and a larger price elasticity of demand is more likely to employemission taxes. The intuition behind this is as follows. When e2 and/or ζ2 are large, country 2’sGHG emissions are large. Also carbon leakage caused by country 1’s environmental regulationis large. By adopting emission quotas, country 1 can induce country 2 to strengthen the envi-ronmental regulation (recall Proposition 8) and mitigate GHG emissions and carbon leakage.

24 A mixed-strategy equilibrium is easily obtained. See Appendix A.4.


Analogously, when e1 and/or ζ1 are small, country 1’s GHG emissions and carbon leakagecaused by country 2’s environmental regulation are small. This implies that even if country 2can induce country 1 to strengthen the environmental regulation by employing emission quotas,a decrease in the country 1’s emission is relatively small. Thus, country 2 has less incentive toemploy emission quotas or tougher environmental regulations.

We should also mention that since all equilibria are noncooporative, they may not achieve thefirst-best outcome from the welfare viewpoint. For example, suppose that both dR1Q(t2)/dt2 <

e2ζ2/e1(1 − ζ1) and dR2Q(t1)/dt1 < e1ζ1/e2(1 − ζ2) hold. Then, EQQ is realized as a subgameperfect Nash equilibrium. However, the best equilibrium among four equilibria is EQT forcountry 1 and is ETQ for country 2. Furthermore, even if both countries employ emissionquotas, they can improve welfare by simultaneously lowering their quota levels from those atEQQ (recall Proposition 6).

7. CONCLUSION

In this article, we explored environmental policy choices in the presence of internationalcarbon leakage caused by fuel price changes, explicitly taking into account international tradein fossil fuel. We considered a world consisting of two fuel-consuming countries emitting GHGand a fuel-producing country. The fuel-consuming countries noncooperatively regulate GHGemissions through emission taxes or quotas. The two policy instruments are equivalent foreach country if the other country’s choice of policy instrument is given. However, the presenceof the carbon-leakage effect affects each country’s policy stance on global warming once theother country switches its policy instrument. That is, nonequivalence between emission taxesand quotas could arise. In particular, we pointed out that in the presence of carbon leakage,environmental quotas are a more stringent policy instrument than environmental taxes in thesense that environmental quotas strengthen environmental regulations in the other country.

Such strategic nonequivalence affects the subgame perfect equilibrium when the countriescommit to either emission taxes or quotas before determining their specific level. We examinewhich combination of instruments emerges as a subgame perfect Nash equilibrium for ourfull game and obtain three pure-strategy equilibria: (i) both countries always choose emissionquotas; (ii) one country always chooses emission quotas and, given this, the other choosesemission taxes; and (iii) neither country has fixed preferences for policy instruments, but bothwant to choose the different instruments from the other’s choice. This result sheds new light onthe question of why adopted policy instruments could be different among countries.

As an illustration of the implications of the results obtained here, we may regard country 1as North (developed countries with better environmental technologies) and country 2 as South,because developed countries such as Japan and Germany have been leading the R&D of carboncapture and storage (CCS) technologies. When only North introduces or tightens environmentalregulations, there is a danger that world total GHG emissions increase, instead of decrease, thusaggravating global warming. This corresponds to the situation with the Kyoto Protocol, in whichonly Annex I Parties are legally obligated to decrease GHG emissions. What would be requiredis to call on South to cooperate with North in dealing with global warming. Thus, the DurbanPlatform, in which all major emitters are required to prepare some measures to control GHGemissions, is a step in the right direction. However, this step is not sufficient, because countrieshave noncooporatively chosen an emission regulation and its specific level. Our policy choicegame captures this aspect. In particular, our result suggests a reason why South (particularly,large emitters with worse environmental technologies) tends to employ emission taxes, whereasNorth tends to adopt emission quotas. Adopting an emission quota in the presence of carbonleakage, North can induce South to strengthen the level of South’s environmental regulation. Onthe other hand, since carbon leakage caused by South’s environmental regulation is relativelysmall, South has less incentive to adopt a tough regulation, that is, emission quotas. Thismay explain why the EU employs an emission quota whereas India and China employ anemission tax.


We should mention that even if both countries take environmental regulations, a realizedequilibrium under noncooporative choices does not lead to Pareto optimum. Thus, policycoordination should be secured. Moreover, in our analysis, North’s environmental regulationsworsen global warming only if environmental technologies are different between North andSouth. The technology gap can be reduced by technology transfer from North to South. Thus,technology transfer plays an important role in dealing with global warming.

The purpose of this article was to present a simple, stylized model in order to focus onthe international carbon leakage caused by changes in the fuel price. To do so, we assumedthat the production of the nontradable good alone is responsible for GHG emissions and thatthe fuel-producing country does not emit GHG. Although we conjecture that our insights arestill valid in more generalized models, it would be worthwhile to examine the implicationsof our approach in those models. Another restrictive assumption is that emission coefficientsare exogenous and country-specific parameters. Since the investment in CCS takes time andhas been led by developed countries, this assumption may be justified to some extent. How-ever, the choice of emission regulations could affect the investment behavior and vice versa.The relationship between emission regulations and technological decisions is an interestingresearch topic to pursue, but it is beyond the scope of our analysis and is left for a futureinvestigation.

APPENDIX

A.1. Proof of zW1 + zW

2 < 0 . This section proves Lemma 2. Equation (15) shows

zWi = �reiζi{ejζj − ei(1 − ζi)},

which yields

1�r

(zW

1 + zW2

) = 2e1e2ζ1ζ2 − e21ζ1(1 − ζ1) − e2

2ζ2(1 − ζ2).

Consider the right-hand side as a quadratic equation in e1. Then, the associated determinant isequal to

ζ21ζ

22e2

2 − ζ1ζ2(1 − ζ1)(1 − ζ2)e22 = e2

2ζ1ζ2(ζ1 + ζ2 − 1) < 0,

which implies that the given equation never becomes nonnegative given e1e2 �= 0. This estab-lishes

zW1 + zW

2 < 0.

A.2. Proof of ∂wiT /∂tj > 0. In this section, we prove Proposition 4. By construction of thewelfare function, one can derive

∂wiT

∂tj= ∂wi

∂tj+ ∂wi

∂rrj = ∂wi

∂tj− rj

ri

∂wi

∂ti

= − θiD′zjt − f j

t

f it

(ti − θiD′)zit = −f j

t {θiD′ej + (ti − θiD′)ei}

= − f jt

{θiD′ej + ei

{f i

(ri

zii

)+ θiD′

(zj

i

zii

)}},


or, alternatively,

− zii

f jt

∂wiT

∂tj= eif iri + ejθiD′zi

i + eiθiD′zji

= eif i(−eiζi) + ejθiD′ × e2i (1 − ζi)f i

r + eiθiD′(−eiejζifjr )

= − e2i f iζi + e2

i ejθiD′(1 − ζi)f ir − e2

i ejθj D′ζifjr .

Thus,

− 1

e2i

zii

f jt

∂wiT

∂tj= −f iζi + �rejθiD′(ζiζj − ζi(1 − ζi))

= − f iζi − �rejθiD′ζiζs < 0,

which establishes

∂wiT

∂tj> 0.

A.3. Proof of Unilateral Equivalence. To prove the unilateral equivalence between emissiontaxes and quotas, we must show that there is a one-to-one relationship for each fuel-consumingcountry between the emission tax rate and the emission quota given the other. Let us prove thisfirst for the case in which the other country chooses emission taxes.

Given country j ’s emission tax rate tj , let qi denote the emission quota or GHG emissions bycountry i. The equilibrium condition requires

qi = eif i(r, ti), s(r) = qi

ei+ zj (r, ti).

Solving the second equation for the fuel price and denoting the solution by rT (qi, tj ), the lattersatisfies

∂rT (qi, tj )∂qi

= 1

ei(s′(r) − ej fjr )

> 0.

Insert this relation into the first equation and solve the latter for the equilibrium emission taxrate or emission permit price ti. Let tiT (qi, tj ) express the solution. It satisfies

∂tiT (qi, tj )∂qi

= eif it

1 − eif irrT

q< 0,

by virtue of (8). This establishes the result.Next, consider the case in which the other country chooses emission quotas. Let qj denote

country j ’s emission quota. Then again the equilibrium requires

qk = ekf k(r, tk), s(r) =∑

k

qk

ek.

The equilibrium fuel price depends on the quota profile q. We express this relation by rQ(q). Itsatisfies

∂rQ(q)∂qi

= 1eis′(r)

> 0.


Insert this into the first equation. Then the emission tax rate is determined by the quota profile,the relation of which we express by ti(q). It satisfies

∂ti(q)∂qi

=1 − eif i

r∂rQ(q)

∂qi

eif it

< 0,

which establishes the result.

A.4. Subgame Perfect Nash Equilibrium. We first obtain Figure 6 by examining each regionin Figure 5. In Regions I, II, V, and IV, we have

EQQ 1ETQ, EQT 1 ETT ,(A.1)

EQQ 2EQT , ETQ 2 ETT .(A.2)

(A.1) ((A.2)) means a quota policy is the dominant strategy for country 1 (2). Thus, a quotapolicy is the dominant strategy for both countries, so that EQQ arises.

In Regions III and VI, since (A.2) holds, a quota policy is the dominant strategy for country2. Thus, we only need to check which policy country 1 prefers when country 2 chooses quotas.Since ETQ 1 EQQ, ETQ arises. The choice of a quota policy dominates that of a tax policy forcountry 2, but country 1 prefers emission taxes when country 2 chooses quotas, so that ETQ

arises.Similarly, in Regions VII and VIII, since (A.2) holds, a quota policy is the dominant strategy

for country 1. Thus, we only need to check which policy country 2 prefers when country 1chooses quotas. Since EQT 2 EQQ, EQT arises. The choice of a quota policy dominates that ofa tax policy for country 1, but country 2 prefers emission taxes when country 1 chooses quotas,so that EQT arises.

In Region IX, we have ETQ 1 EQQ 1 EQT 1 ETT and EQT 2 EQQ 2 ETQ 2 ETT ,which implies that each country is better off by choosing a policy instrument different fromthe other’s choice. Thus, there are at least three equilibria; two are pure-strategy equilibria,ETQ and EQT , and the last is a mixed-strategy equilibrium.

Next we obtain a mixed-strategy equilibrium in Region U in Figure 6. Let ρTj denote the

probability that country j chooses emission taxes. Then country i is indifferent between taxesand quotas if and only if

ρTj wi

QiTj+ (

1 − ρTj

)wi

QQ = ρTj wi

TT + (1 − ρT

j

)wi

TiQj,

where wiTiQj

, for example, represents country i’s equilibrium welfare when country i choosesemission taxes and country j emission quotas. The above equation shows that the equilibriumprobability ρT

j satisfies

ρTj =

wiTiQj

− wiQQ

(wiQiTj

− wiTT ) + (wi

TiQj− wi

QQ).

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ENVIRONMENTAL MANAGEMENT POLICY UNDER INTERNATIONAL CARBON LEAKAGE